A consistent model selection procedure for Markov random fields based on penalized pseudolikelihood

Ji, Chuanshu; Seymour, Lynné

doi:10.1214/aoap/1034968138

Cited by 41 publications

(26 citation statements)

References 19 publications

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“…In particular, it can be proven that some of the 1 -based approaches are consistent for model selection under particular scalings of the graph size, degrees, and number of samples [10], [14]; for the case where each degree is bounded by d, a similar consistency analysis has been performed for a heuristic method in the paper [4]. Other researchers [8], [6] have analyzed model selection criteria based on pseudolikelihood.…”

Section: Introductionmentioning

confidence: 99%

Information-theoretic limits of graphical model selection in high dimensions

Santhanam

Wainwright

2008

2008 IEEE International Symposium on Information Theory

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The problem of graphical model selection is to correctly estimate the graph structure of a Markov random field given samples from the underlying distribution. We analyze the information-theoretic limitations of this problem under high-dimensional scaling, in which the graph size p and the number of edges k (or the maximum degree d) are allowed to increase to infinity as a function of the sample size n. For pairwise binary Markov random fields, we derive both necessary and sufficient conditions on the scaling of the triplet (n, p, k) (or the triplet (n, p, d)) for asympotically reliable reocovery of the graph structure.

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Section: Introductionmentioning

confidence: 99%

Information-theoretic limits of graphical model selection in high dimensions

Santhanam

Wainwright

2008

2008 IEEE International Symposium on Information Theory

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“…We propose the use of a criterion derived from the BIC. A similar approach was used by [12] for choosing between different Markov random field models in the case where the true scene is directly observed and the number of segments is known in advance; neither of these is the case in the applications we have in mind. When, as here, the true scene is not observed, this would require evaluation of the likelihood of the observed data, LðY jKÞ, namely,…”

Section: Penalized Pseudolikelihood Criterion: Plicmentioning

confidence: 99%

Approximate Bayes factors for image segmentation: the Pseudolikelihood Information Criterion (PLIC)

Stanford

Raftery

2002

IEEE Trans. Pattern Anal. Machine Intell.

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Abstract-We propose a method for choosing the number of colors or true gray levels in an image; this allows fully automatic segmentation of images. Our underlying probability model is a hidden Markov random field. Each number of colors considered is viewed as corresponding to a statistical model for the image, and the resulting models are compared via approximate Bayes factors. The Bayes factors are approximated using BIC (Bayesian Information Criterion), where the required maximized likelihood is approximated by the Qian-Titterington pseudolikelihood. We call the resulting criterion PLIC (Pseudolikelihood Information Criterion). We also discuss a simpler approximation, MMIC (Marginal Mixture Information Criterion), which is based only on the marginal distribution of pixel values. This turns out to be useful for initialization and it also has moderately good performance by itself when the amount of spatial dependence in an image is low. We apply PLIC and MMIC to a medical image segmentation problem.Index Terms-BIC, color image quantization, ICM algorithm, image segmentation, Markov random field, medical image, mixture model, posterior model probability, pseudolikelihood, satellite image.

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“…Therefore, it is reasonable to consider a penalized MPL to estimate the basic neighborhood of Markov random fields. Indeed, Smith and Miller formulated this conjecture [23] and Ji and Seymour proved the weak consistency of the estimator assuming the prior information of a finite set of possible basic neighborhoods [19]. Csiszár and Talata proved the strong consistency of the estimator without prior information [6].…”

Section: Introductionmentioning

confidence: 98%

Markov neighborhood estimation with linear complexity for random fields

Talata

2014

2014 IEEE International Symposium on Information Theory

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Markov random fields on the d-dimensional integer lattice with finite state space are considered, and the problem of estimation of the basic neighborhood from a single realization observed in a finite region is addressed. The Optimal Likelihood Ratio (OLR) estimator is introduced. Its nearly linear computation complexity is shown, and a bound on the probability of the estimation error is proved that implies strong consistency.

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A consistent model selection procedure for Markov random fields based on penalized pseudolikelihood

Cited by 41 publications

References 19 publications

Information-theoretic limits of graphical model selection in high dimensions

Information-theoretic limits of graphical model selection in high dimensions

Approximate Bayes factors for image segmentation: the Pseudolikelihood Information Criterion (PLIC)

Markov neighborhood estimation with linear complexity for random fields

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